In this paper, we study two stochastic problems for time-fractional Rayleigh-Stokes equation including the initial value problem and terminal problem. Here, are perturbed by Wiener process, fractional derivative taken in sense of Riemann-Liouville, source function time-spatial noise nonlinear satisfy globally Lipschitz conditions. We attempt to give some existence r...

In this paper, we introduce the new class of implicit L-stable generalized hybrid methods for the numerical solution of first order initial value problems. We generalize the hybrid methods with utilize ynv directly in the right hand side of classical hybrid methods. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the n...

The focus of the present study is the BBM equation which models unidirectional propagation of small amplitude, long waves in dispersive media. This evolution equation has been used in both laboratory and field studies of water waves. The principal new result is an exact theory of convergence of the two-point boundary-value problem to the initial-value problem posed on an infinite stretch of the...

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We consider initial value/boundary value problems for fractional diffusion-wave equation: ∂ α t u(x, t) = Lu(x, t), where 0 < α ≤ 2, where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of ths weak solutions and the asymptotic behaviour as the time t goes to ∞ and the proofs are based on the eigenfunction expansions. ...